Granular Instrumental Variables

我建议对粒度工具变量（GIV）进行方法学研究。我的研究将集中在扩展这个新兴领域的理论基础上。GIV方法从面板数据（在许多不同时间段（T）观察到的许多个体（N））构建工具，以估计具有内生回归量的结构时间序列模型（Gabaix和Koijen，2021）。仪器的构造取决于误差的因素结构和设置的“粒度”。也就是说，未观察到的错误具有潜在因素和特质成分，潜在因素的影响因个体而异。颗粒设置的特征在于，除了在完全竞争的情况下的无限小的代理之外，其影响不可忽略的几个大代理（Gabaix，2009）。具有内源性回归量的面板需要外部工具进行一致的估计（Ahn等人，2013; Bai和Ng，2010; Bai，2009）。但这种工具很难找到，往往需要对个人环境有深入的了解。GIV是有前途的，因为我们从系统内构建经济直观和有效的工具。当N很小，T很大（有限面板）和当N和T都很大（大面板）时，可以构建GIV。这导致了有趣的应用在宏观经济学和实证金融分别。GIV方法的核心思想是特质误差的线性变换是估计内生变量的有效工具。关键的方法学挑战是，我们不单独观察这些特质误差项。但作为一个新的研究领域，GIV的方法论研究还很有限。Gabaix和Koijen（2021）阐述了固定N和大T的思想和渐近理论。Banafti和Lee（2022）将这一点扩展到大N和T设置。这为GIV方法的估计和推断的方法学研究铺平了道路，重点是一致的因素估计，工具弱点，最佳工具，过度识别，等等。大面板：N和T大，和2。有限的面板：研究流1：大型小组在这个研究流下，我将承担先进的推理问题，如仪器的弱点，最佳仪器，和高估。我也将比较GIV与其他可能的估计沿着这些角度。仪器的弱点是任何IV设置中的主要问题之一（Andrews等人，2019年;股票和赖特，2000年;安托万和雷诺，2021年）。Banafti和Lee（2022）表明，当市场份额的分布没有足够的厚尾时，工具和外生变量之间的第一阶段关系变得非常弱。同样，弱因子/因子载荷的存在会影响Bai和Ng（2023）工具的质量。我建议发展弱工具和弱因素下GIV的识别和推断理论，目前还没有统一的最优GIV理论。我将从渐近有效性的角度探讨最优GIV的问题。我也将致力于广义矩法（GMM）估计使用over-identified estimators.研究流2：有限面板在有限的面板，我们有一小部分人谁观察了很多次。一个例子是欧元区国家（N = 12）主权债务30年（T = 12 x 30 = 360）的月收益率。从（1）中的面板构建GIV取决于我们隔离特质冲击的能力。

I propose to conduct methodological research on Granular Instrumental Variables (GIV). Myresearch will focus on expanding the theoretical foundations of this fledgling area of inquiry. I will apply my results to analyze suitable empirical applications.The GIV methodology constructs instruments from panel data (many individuals (N) observed at many different time periods (T)) to estimate structural time series models with endogenous regressors (Gabaix and Koijen, 2021). The construction of instruments depends on the factor structure of the error and the 'granularity' of the setting. That is, the unobserved error has latent factors and an idiosyncratic component, with the effect of the latent factor varying across individuals. Granular settings are characterized by a few large agents whose impact is not negligible, in addition to infinitesimal agents, as in the case of perfect competition (Gabaix, 2009).Panels with endogenous regressors require external instruments for consistent estimation (Ahn et al., 2013; Bai and Ng, 2010; Bai, 2009). But such instruments are very difficult to find and may often require a deep understanding of the individual setting. GIV is promising as we construct economically intuitive and valid instruments from within the system. GIV can be constructed when N is small, T is large (limited panel) and when both N and T are large (large panels). This leads to interesting applications in macroeconomics and empirical finance respectively. The core idea of the GIV methodology is that a linear transformation of the idiosyncratic errors is a valid instrument for the estimation of the endogenous variable. The key methodological challenge is that we do not separately observe these idiosyncratic error terms. But as a new area of research, the methodological work on GIV is very limited. Gabaix and Koijen (2021) lay out the idea and the asymptotic theory for fixed N and large T. Banafti and Lee (2022) extend this to the large N and T setting. This paves the way for methodological research about the estimation and inference of the GIV methodology with a focus on consistent factor estimation, instrument weakness, optimal instruments, over-identification, and so on. I propose to answer questions in this research setting under two streams: 1. Large panels: N and T large, and 2. Limited panels: N fixed, and T large.Research Stream 1: Large PanelsUnder this research stream, I will undertake advanced inferential issues like weakness of instrument, optimal instrument, and over-estimation. I will also compare GIV with other possible estimators along these angles. Weakness of the instrument is one of the primary concerns in any IV setting (Andrews et al., 2019; Stock and Wright, 2000; Antoine and Renault, 2021). Banafti and Lee (2022) show that when the distribution of market shares does not have sufficiently fat tails, the first stage relationship between the instrument and the exogenous variable becomes very weak. Similarly, the presence of weak factors/factor loadings can affect the quality of the instruments Bai and Ng (2023). I propose to develop the theory for the identification and inference of GIV under weak instruments and factors.There is not yet a unified theory of optimal GIV. I will be exploring the question of optimal GIV from the point of view of asymptotic efficiency. I will also be working on Generalized Method of Moments (GMM) estimation using over-identified estimators.Research Stream 2: Limited PanelsIn limited panels, we have a small number of individuals who are observed many times. An example is the monthly yields on the sovereign debt of Eurozone countries (N = 12) observed for 30 years (T = 12 x 30 = 360). The construction of the GIV from the panel in (1) depends on our ability to isolate the idiosyncratic shocks.